For location work, such as in offices and houses, is there any merit to placing a mat underneath a lightstand to protect the floor against bulb shatters? This would be a heat-resistant mat, or even a small sheet of plywood, to prevent a rug or wood floor from burns should a bulb shatter and fall out of a lightbox.

Does anyone use such an item? Or, is the likelihood of a 300/500/650 watt bulb causing damage so low that this kind of protection is not needed?

It's not low enough to ignore. Many lights have a safety scrim over them. If your's does, that's the best insurance. Otherwise, I'd look into some Nomex cloth as a ground sheet.

Mike,
Thanks. Do you use this material, and can you recommend a retail supplier? I haven't found it at B&H or other lighting equipment suppliers.
The Chimera 8000 kit and the Lowel Rifa lights use a bulb without a metal screen. The one with the Chimera is double-walled for safety, and I imagine the Starlight bulbs are as well. I'm just wondering if the double wall of glass is as effective as a metal screen or scrim in protecting against bulb explosions.

In Hollywood there are specialists who do nothing by "layout."
That's covering the unshown (to the camera) floor with cardboard
so as to protect it, not only from stuff like lamps shattering (infrequent)
but from dirty shoes, road trunks, etc.

Cardboard would be cheap and easier than expensive cloth
which is easy to stumble over. Recycle it when done . . . all good.

Cardboard might be cheaper but it is as inflamable as the rug. A Fire Marshal wouldn't be happy to see flamable material spread around a work area.

I'd probably go to the nearest Welding Supply and ask for a Welding Blanket.

If you don't live near one, you could try these folks who I found with a Google search. I know nothing about them.

http://www.wilsonindustries.com/automotive_sub_blankets.html

Cardboard would seem as if it would be a fire hazard, but actually
when laid flat it isn't that easy to catch fire and provides a good
thermal shield as well. Glass blowers handle near molten glass with dry
(thick) newspaper. An old bar trick is to challenge someone
to hold a $20 bill against their hand. Light a cigarette and tell them
that if the cigarette burns through the paper money before they
pull their hand away from the heat, they can keep it, but if they
pull away they have to pay $20. Their hand will be a lump of cooked meat before
the cigarette will burn through.

IMO, there is no way a blown lamp could
cause properly installed (flat and taped) cardboard to catch on fire
before it cooled. That's why cardboard is used by the industry.

IMHO, blankets spread on the floor are far more dangerous as a trip
hazard.

I'd bet the $20 bill you could not convince the local fire marshal of the inflamability of untreated cardboard in that application, industry practice or not.